What is learned during perceptual learning? We address this question by analyzing how perceptual inefficiencies improve over the course of perceptual learning (Dosher & Lu, 1998). Systematic measurements of human performance as a function of both the amount of external noise added to the signal stimulus and the length of training received by the observers enable us to track changes of the characteristics of the perceptual system (e.g., internal noise[s] and efficiency of the perceptual template) as perceptual learning progresses, and, therefore, identifies the mechanism(s) underlying the observed performance improvements. Two different observer models, the linear amplifier model (LAM) and the perceptual template model (PTM), however, have led to two very different theories of learning mechanisms. Here we demonstrate the failure of an LAM-based prediction – that the magnitude of learning-induced threshold reduction in high external noise must be less or equal to that in low external noise. In Experiment 1, perceptual learning of Gabor orientation identification in fovea showed substantial performance improvements only in high external noise but not in zero or low noise. The LAM-based model was “forced” to account for the data with a combination of improved calculation efficiency and (paradoxical) compensatory increases of the equivalent internal noise. Based on the PTM framework, we conclude that perceptual learning in this task involved learning how to better exclude external noise, reflecting retuning of the perceptual template. The data provide the first empirical demonstration of an isolable mechanism of perceptual learning. This learning completely transferred to a different visual scale in a second experiment.

*E*, an equivalent additive internal noise

*N*

_{eq}, and a decision stage (Ahumada & Watson, 1985; Barlow, 1956; Burgess et al., 1981; Nagaraja, 1964; Pelli, 1981). The concept of perceptual or calculation efficiency is not well understood; however, it is usually interpreted as a reflection of the ability of the observer to utilize sensory information. The equivalent additive noise determines the absolute threshold for the observer.

*E*

_{τ}in Equation 1 depends on the performance level upon which threshold is defined. Whereas Equation 1 often provides excellent accounts of psychophysical data at a single performance level in a wide range of perceptual tasks (for a review, see Burgess et al., 1999), it in general fails to account for human behavior at multiple performance levels, even with a reasonable elaboration that relates

*E*

_{τ}to the corresponding performance levels (Lu & Dosher, 1999).

*E*

_{eq}) and the calculation efficiency (

*E*

_{τ}), there are essentially two possible ways perceptual learning can improve the performance (reducing thresholds) of the model: (1) increasing calculation efficiency, which results in threshold reduction with equal magnitude (in log) across the full range of external noise levels (Figure 1b), and/or (2) reducing equivalent internal noise, which results in threshold reduction restricted in low external noise conditions (Figure 1c). Therefore, a “pure” efficiency account of perceptual learning (e.g., Gold et al., 1999) predicts perceptual improvements with equal magnitude across all the external noise levels, a prediction rejected by Dosher and Lu (1999).

_{γ}, (3) a multiplicative Gaussian internal noise whose SD is proportional (with a factor of

*N*

_{mul}) to the total energy in the stimulus after the nonlinear transformation, (4) an additive internal noise whose amplitude (

*N*

_{add}) is independent of the stimulus strength, and (5) a decision process (see Lu & Dosher, 1999, for the formal development and quantitative tests for the form of the PTM model). In the PTM, threshold signal contrast at a particular performance level (i.e.,

*d*′) is expressed as a function of external noise contrast

*N*

_{ext}:

*stimulus enhancement*reduces absolute thresholds by reducing internal additive noise;

*perceptual template retuning*optimizes the perceptual template to exclude external noise or distractors; and

*contrast-gain control*reduction decreases the impact of internal multiplicative noise. These three mechanisms exhibit signature performance patterns (Figure 2) when we compare TVC functions at several points during perceptual learning (Dosher & Lu, 1999).

*Stimulus enhancement*increases the relative (vs. internal additive noise) gain of both the signal and the external noise in the stimulus and is associated with performance improvements only in low or zero external noise (Figure 2b).

*Perceptual template retuning*improves the ability of the observer to exclude external noise and therefore is associated with performance improvements only in high external noise (Figure 2c).

*Contrast-gain control reduction*increases system response to stimulus contrast and is associated with improvements throughout the full range of external noise (Figure 2d). In addition, we can distinguish various mechanism mixtures by measuring TVC functions at multiple performance levels (e.g., 70% and 80% correct).

^{2}) into 6144 distinct gray levels (12.6 bits). The display was gamma corrected using a psychophysical procedure (Lu & Sperling, 1999). All displays were viewed binocularly with natural pupil at a viewing distance of approximately 72 cm in Experiment 1 and 36 cm in Experiment 2 in a dimly lighted room.

*l*

_{0}= 27 cd/m

^{2}, Gabor center frequency

*f*= 1.34 c/deg, and Gabor spatial window

*σ*= 0.75 deg. The peak contrast

*c*was set by the adaptive staircase procedures.

*d*′ of 1.089) performance level.

*η*, but independent

*α*’s, were fit to the five data sets in each external noise condition. Thresholds at

*Pc*= 70.7% and

*Pc*= 79.3% were computed from the psychometric functions in order to quantify threshold versus external noise contrast functions.

*E*

_{τ}in learning block

*t*by a learning parameter

*E*

_{Eτ}(

*t*). This learning parameter may in general depend on the performance level on which threshold is defined. If this dependency on criterion performance level occurs, this represents a failure of parameter consistency of the model. The second mechanism, perceptual learning-induced internal noise reduction, is modeled by multiplying the equivalent internal noise by

*E*

_{eq}(

*t*). From Equation 1, we have

*A*

_{eq}= 1.0 and

*A*

_{E70.7%}(1) =

*A*

_{E79.3%}(1) = 1. This simply scales all learning in relation to the initial performance level. A full model of the data collected in Experiment 1, therefore, consists of

*N*

_{eq},

*E*

_{70.7%},

*E*

_{79.3%},

*A*

_{eq}(2,…,5),

*A*

_{E70.7%}(2,…,5), and

*A*

_{E79.3%}(2,…,5), a total of 15 parameters.

*t*by a learning parameter

*A*

_{f}(

*t*); (2) stimulus enhancement amplifies the stimulus (both the signal and the external noise). This is mathematically equivalent to reducing internal additive noise by

*A*

_{a}(

*t*) (Lu & Dosher, 1998); (3) changes in contrast-gain control properties result in a reduction of internal multiplicative noise by

*A*

_{m}(

*t*) Equation 2 can be modified to incorporate the learning parameters as follows:

*A*

_{a}(1) = 1,

*A*

_{f}(1) = 1, and

*A*

_{m}(1) = 1. A full model of the data collected in Experiment 1 therefore consists of

*N*

_{a},

*N*

_{m},

*β*,

*γ*,

*A*

_{a}(2,…,5),

*A*

_{f}(2,…,5), and

*A*

_{m}(2,…,5), a total of 16 parameters.

*A*

_{E70.7%}(

*t*) and

*A*

_{E79.3%}(

*t*)), (4) improved efficiencies with same magnitudes at different performance levels (

*A*

_{E70.7%}(

*t*) =

*A*

_{E79.3%}(

*t*)), (5) a combination of (2) and (3), and (6) a combination of (2) and (4). In addition, eight forms of the PTM-based models were considered, ranging from no change of any learning parameter with increased training to changes of all the learning parameters with increased learning.

*r*

^{2}statistic where Σ and

*mean*() were across all the practice and external noise conditions at both performance levels. Of the six LAM-based and eight PTM-based models, some are reduced models (proper subsets) of the others.

*F*-tests for nested models were used to compare these models: where

*df*

_{1}=

*k*

_{full}−

*k*

_{reduced}, and

*df*

_{2}=

*N*−

*k*

_{full}. The

*ks*are the number of parameters in each model, and

*N*is the number of predicted data points. The minimal yet sufficient (i.e., statistically equivalent to the maximum) model was selected as the best-fitting model for the data, separately for the LAM-based and the PTM-based model lattices.

*Pc*= 70.7% and

*Pc*= 79.3%) were estimated in each external noise condition using adaptive staircase procedures (Figure 3d and 3e). This design yielded a total of 20 [10 sessions × 2 criterion levels] TVC functions, each sampled at eight external noise levels. The average of these TVC functions across all the observers are shown in Figure 4, pooled over every two sessions.

*A*

_{E70.7%}(

*t*) =

*A*

_{E79.3%}(

*t*) and increased equivalent internal noise provided the best fit. With 11 parameters and r

^{2}= 0.9915, this model is statistically equivalent to the most saturated model (F(4,65)=0.0031,

*p*> .95) and is superior to all the models with fewer learning mechanisms: (1) F(4,69)=7.542,

*p*< 5 × 10

^{−5}, for a comparison with the model that assumes modifications of calculation efficiency but constant internal noise across training sessions; (2) F(4, 69)=22.72,

*p*< 10

^{−11}, for a comparison with the model that assumes internal noise changes but constant calculation efficiency across training sessions; and (3) F(8,69)=12.12,

*p*< 10

^{−9}, for a comparison with the model that assumes no learning at all. The parameters of the best-fitting model are shown in Table 1.

Parameter | Value | SE |
---|---|---|

N_{eq} | 0.0417 | 0.0013 |

E_{70.7%} | 0.3484 | 0.0122 |

E_{79.3%} | 0.2261 | 0.0078 |

A_{eq}(2) | 1.114 | 0.051 |

A_{eq}(3) | 1.389 | 0.064 |

A_{eq}(4) | 1.451 | 0.066 |

A_{eq}(5) | 1.374 | 0.064 |

A_{E}(2) | 1.234 | 0.057 |

A_{E}(3) | 1.697 | 0.083 |

A_{E}(4) | 1.979 | 0.096 |

A_{E}(5) | 1.949 | 0.099 |

^{2}= 0.9915, this model is statistically equivalent to the fullest model that assumes all three perceptual learning mechanisms (F(8,64)=0.5582,

*p*> .75) and is superior to the model that assumes no perceptual learning at all (F(4,72)= 12.63,

*p*< 10

^{−7}). The parameters of the best-fitting model are shown in Table 2.

Parameter | Value | SE |
---|---|---|

N_{add} | 0.00115 | 0.00041 |

N_{mul} | 0.037 | 0.081 |

β | 0.579 | 0.011 |

γ | 2.185 | 0.1348 |

A_{f}(2) | 0.907 | 0.020 |

A_{f}(3) | 0.783 | 0.018 |

A_{f}(4) | 0.729 | 0.017 |

A_{f}(5) | 0.729 | 0.016 |

*A*

_{f}values for the training sessions in Figure 4b.

*p*> .25). This suggests a complete transfer of perceptual learning of the orientation identification task at fovea to a viewing distance at half of the original. If transfer had not been complete, practice at the new scale would have produced new learning, which was not observed. In other words, perceptual learning of this task is scale invariant in the range tested (1 to 2). The best-fitting model has four parameters (

*N*

_{add}, (

*N*

_{mul},

*β, γ*) with r

^{2}= 0.9959.

*perceptual template*retuning mechanism of perceptual learning in a psychophysical study. The results are important for theories of perceptual learning because they behaviorally demonstrate the existence of an isolable mechanism. Much as the spectroscopic methods of atomic physics enabled physicists to unravel the structure of atoms, applications of the external noise method will enable us to discover the different mechanisms of perceptual learning.